Question

Given the table below, which of the following statements is true?

Line Equation
Line A y=−12x−2
Line B y=2x−3
Line C y=12x+2
Line D y=2x+5



(1 point)
Responses

Line C is perpendicular to Line D
Line C is perpendicular to Line D

Line B is perpendicular to Line D
Line B is perpendicular to Line D

Line A is perpendicular to Line C
Line A is perpendicular to Line C

Line A is perpendicular to Line B
Line A is perpendicular to Line B
Skip to navigation

Answer 1

To determine which statements are true regarding the perpendicularity of the given lines, we need to look at the slopes of each line from their equations.

1. **Line A:** \(y = -12x - 2\)
- Slope (m) = -12

2. **Line B:** \(y = 2x - 3\)
- Slope (m) = 2

3. **Line C:** \(y = 12x + 2\)
- Slope (m) = 12

4. **Line D:** \(y = 2x + 5\)
- Slope (m) = 2

Two lines are perpendicular if the product of their slopes equals -1.

Now we can evaluate the pairs given in the statements:

- **Line A (slope -12)** and **Line B (slope 2)**:
\[
-12 \times 2 = -24 \quad (\text{not perpendicular})
\]

- **Line A (slope -12)** and **Line C (slope 12)**:
\[
-12 \times 12 = -144 \quad (\text{not perpendicular})
\]

- **Line B (slope 2)** and **Line D (slope 2)**:
\[
2 \times 2 = 4 \quad (\text{not perpendicular})
\]

- **Line C (slope 12)** and **Line D (slope 2)**:
\[
12 \times 2 = 24 \quad (\text{not perpendicular})
\]

Since none of the pairs produce a product of -1, none of the statements about perpendicularity among the lines provided is true.

Therefore, **all the statements provided are false**.